Year: 2026
Type: preprint
Abstract: We construct an explicit smooth projective Fano fourfold $X$ over an algebraically closed field $k$ of characteristic two with $H^1(X,\mathcal{O}_X)\simeq k$. Moreover, $X$ does not admit any free rational curve, and so it is not separably uniruled. The example has been constructed using ChatGPT.
Source: arXiv (Cornell University)
Authors: Waldron, Joe, Witaszek, Jakub
Institutions: Northwestern University, Michigan State University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
Awards: Birational classification of varieties: connections to arithmetic and algebra, Positive and Mixed Characteristic Birational Geometry and its Connections with Commutative Algebra and Arithmetic Geometry, CAREER: New Frontiers in Birational Geometry - Novel Arithmetic Techniques and Applications
OpenAlex ID: W7214362260